Slow Diffusion by Singlet State NMR Spectroscopy

A dual-core NMR system for field-cycling singlet assisted diffusion NMR

Long-lived singlet spin order offers the possibility to extend the spin memory by more than an order of magnitude. This enhancement can be used, among other applications, to assist NMR diffusion experiments in porous media where the extended lifetime of singlet spin order can be used to gain information about structural features of the medium as well as the dynamics of the imbibed phase. Other than offering the possibility to explore longer diffusion times of the order of many minutes that, for example, gives unprecedented access to tortuosity in structures with interconnected pores, singlet order has the important advantage to be immune to the internal field gradients generated by magnetic susceptibility inhomogeneities. These inhomogeneities, however, are responsible for very short T₂ decay constants in high magnetic field and this precludes access to the singlet order in the first instance. To overcome this difficulty and take advantage of singlet order in diffusion experiments in porous media, we have here developed a dual-core system with radiofrequency and 3-axis pulsed field gradients facilities in low magnetic field, for preparation and manipulation of singlet order and a probe, in high magnetic field, for polarisation and detection. The system operates in field-cycling and can be used for a variety of NMR experiments including diffusion tensor imaging (both singlet assisted and not). In this paper we present and discuss the new hardware and its calibration, and demonstrate its capabilities through a variety of examples.

Long-Lived States Provide Insights from NMR into the β-Cyclodextrin Drug Assemblies

In the last two decades, extending spin memory in NMR has been used for several purposes. Long-lived states (LLS) or singlet states are one of the first spin memory enhancement techniques used. LLS have the potential to extract structural information and intra- and intermolecular interactions of complex systems other than studying slow phenomenon. The motional regime of β-cyclodextrin (β-CD) drug inclusion complexes generally lies in the intermediate region, where ωτ_c ≈ 1, and the standard methods of studying these interactions, i.e., NOE and chemical shift monitoring, suffer from insufficient output information. The sensitivity of LLS toward the environmental changes is utilized here to gain insights into the drug assemblies formed by β-CD. One can use change in relaxation of LLS to study the structural changes during complexation. The examples of β-CD with the drugs indomethacin, paracetamol, gliclazide, and CI-933 (a precursor 4-methoxybenzamide) were studied. Indomethacin, paracetamol, and 4-methoxybenzamide show strong interaction through the para-substituted benzene ring, unlike gliclazide. Relaxation of LLS in β-CD-drug complexes is modeled using standard Redfield Relaxation Theory. Computational studies performed support the experimental observations. Docking and molecular dynamics simulation provided the explanation of the relaxation properties of these drug molecules.

Long-lived states of methylene protons in achiral molecules

In nuclear magnetic resonance (NMR), the lifetimes of long-lived states (LLSs) are exquisitely sensitive to their environment. However, the number of molecules where such states can be excited has hitherto been rather limited. Here, it is shown that LLSs can be readily excited in many common molecules that contain two or more neighboring CH2 groups. Accessing such LLSs does not require any isotopic enrichment, nor does it require any stereogenic centers to lift the chemical equivalence of CH2 protons. LLSs were excited in a variety of metabolites, neurotransmitters, vitamins, amino acids, and other molecules. One can excite LLSs in several different molecules simultaneously. In combination with magnetic resonance imaging, LLSs can reveal a contrast upon noncovalent binding of ligands to macromolecules. This suggests new perspectives to achieve high-throughput parallel drug screening by NMR.

Polychromatic Excitation of Delocalized Long-Lived Proton Spin States in Aliphatic Chains

Long-lived states (LLS) involving pairs of magnetically inequivalent but chemically equivalent proton spins in aliphatic (CH_{2})_{n} chains can be excited by simultaneous application of weak selective radio frequency fields at n chemical shifts by polychromatic spin-lock induced crossing. The LLS are delocalized throughout the aliphatic chains by mixing of intrapair singlet states and by excitation of LLS comprising products of four and six spin operators. The measured lifetimes T_{LLS} in a model compound are about 5 times longer than T_{1} and are strongly affected by interactions with macromolecules.

31P spin-lattice and singlet order relaxation mechanisms in pyrophosphate studied by isotopic substitution, field shuttling NMR, and molecular dynamics simulation

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for ³¹P spin-lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin-rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin-rotation interaction is a consequence of the relatively rapid rotation of the -PO₃^2- entities around the bridging P-O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin-lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups).

Prediction of 1H Singlet Relaxation via Intermolecular Dipolar Couplings Using the Molecular Dynamics Method

Dissolution dynamic nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tagging to probe slow dynamic processes, and detection of ligand-protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular dipolar, intermolecular dipolar between solvent and solute, chemical shift anisotropy, and spin-rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

Weak nuclear spin singlet relaxation mechanisms revealed by experiment and computation

Nuclear spin singlet states are often found to allow long-lived storage of nuclear magnetization, which can form the basis of novel applications in spectroscopy, imaging, and in studies of dynamic...

Exotic nuclear spin behavior in dendritic macromolecules

Dendrimers are a class of branched, highly symmetric macromolecules that have been shown to be useful for a vast number of different applications. Potential uses as fluorescence sensors, in catalysis and perhaps most importantly in medical applications as drug delivery systems or cytotoxica have been proposed. Herein we report on an exotic behaviour of the nuclear spins in a dendritic macromolecule in the presence of different paramagnetic ions. We show that the stability of the long lived nuclear singlet state, is affected by the presence of Cu(II), whereas other ions did not have any influence at all. This effect could not be observed in the case of a simple tripeptide, in which the nuclear singlet stability was influenced by all investigated paramagnetic ions, a potentially useful effect in the development of Cu(II) selective probes. By adding a fluorescent marker to our molecule we could show that the nuclear singlet multimer (NUSIMER) is taken up by living cells. Furthermore we were able to show that nuclear singlet state NMR can be used to investigate the NUSIMER in the presence of living cells, showing that an application in in vivo NMR can be feasible.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

31P nuclear spin singlet lifetimes in a system with switchable magnetic inequivalence: experiment and simulation

³¹P NMR spectroscopy and the study of nuclear spin singlet relaxation phenomena are of interest in particular due to the importance of phosphorus-containing compounds in physiology. We report the generation and measurement of relaxation of ³¹P singlet order in a chemically equivalent but magnetically inequivalent case. Nuclear magnetic resonance singlet state lifetimes of ³¹P pairs have heretofore not been reported. Couplings between ¹H and ³¹P nuclei lead to magnetic inequivalence and serve as a mechanism of singlet state population conversion within this molecule. We show that in this molecule singlet relaxation occurs at a rate significantly faster than spin-lattice relaxation, and that anticorrelated chemical shift anisotropy can account for this observation. Calculations of this mechanism, with the help of molecular dynamics simulations and ab initio calculations, provide excellent agreement with the experimental findings. This study could provide guidance for the study of ³¹P singlets within other compounds, including biomolecules.

Centralizer theory for long-lived spin states

Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite the growing importance of long-lived spin states in modern NMR, strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper, we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyze long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterization of the centralizer, on the other hand, does not rely on any special symmetry arguments, and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.

Hyperpolarization and the physical boundary of Liouville space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I = 1 / 2 , I = 1 , I = 3 / 2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Nuclear Spin Relaxation of Longitudinal and Singlet Order in Liquid-CO2 Solutions

Hyperpolarization techniques can enormously enhance the NMR signal thus allowing the exploitation of hyperpolarized substrates for in-vivo MRI applications. The short lifetime of hyperpolarized spin order poses significant limitations in such applications. Spin order storage can be prolonged through the use of long-lived spin states. Additionally, the storage of spin polarization-either in the form of longitudinal or singlet order-can be prolonged in low viscosity solutions. Here, we report the use of low viscosity liquid-CO₂ solutions to store nuclear spin polarization in the form of longitudinal and singlet order for extended periods. Our results demonstrate that this storage time can be considerably sustained in liquid-CO₂ solutions in comparison to other low viscosity solvents, opening up the possibility of new, exciting storage experiments in the future.

Single-scan measurements of nuclear spin singlet order decay rates

Measurements of singlet spin order decay rates are time consuming due to the long-lived nature of this form of order and the typical pseudo-2D mode of acquisition. Additionally, this acquisition modality is not ideal for experiments run on hyperpolarized order because of the single-shot nature of hyperpolarization techniques. We present a methodology based on spatial encoding that not only significantly reduces the duration of these experiments but also confers compatibility using spin hyperpolarization techniques. The method condenses in a single shot the variable delay array used to measure decay rates in conventional pseudo-2D relaxation experiments. This results in a substantial time saving factor and, more importantly, makes the experiment compatible with hyperpolarization techniques since only a single hyperpolarized sample is required. Furthermore, the presented method, besides offering savings on time and costs, avoids reproducibility concerns associated with repetition in the hyperpolarization procedure. The method accelerates the measurement and characterization of singlet order decay times, and, when coupled with hyperpolarization techniques, can facilitate the quest for systems with very long decay times.

Symmetry versus entropy: Long-lived states and coherences

In recent years, new molecular symmetry-based approaches for magnetic resonance have been invented. The implications of these discoveries will be significant for molecular imaging via magnetic resonance, in vitro as well as in vivo, for quantum computing and for other fields. Since the initial observation in 2004 in Southampton that effective spin symmetry can be instilled in a molecule during magnetic resonance experiments, spin states that are resilient to relaxation mechanisms have been increasingly used. Most of these states are related to the nuclear singlet in a pair of J-coupled spins. Tailored relaxation rate constants for magnetization became available in molecules of different sizes and structures, as experimental developments broadened the scope of symmetry-adapted spin states. The ensuing access to timescales longer than the classically-attained ones by circa one order of magnitude allows the study of processes such as slow diffusion or slow exchange that were previously beyond reach. Long-lived states formed by differences between populations of singlets and triplets have overcome the limitations imposed by longitudinal relaxation times (T₁) by factors up to 40. Long-lived coherences formed by superpositions of singlets and triplets have overcome the limit of classical transverse coherence (T₂) by a factor 9. We present here an overview of the development and applications of long-lived states (LLS) and long-lived coherences (LLC's) and considerations on future perspectives.

Ultrafast diffusion exchange nuclear magnetic resonance

The exchange of molecules between different physical or chemical environments due to diffusion or chemical transformations has a crucial role in a plethora of fundamental processes such as breathing, protein folding, chemical reactions and catalysis. Here, we introduce a method for a single-scan, ultrafast NMR analysis of molecular exchange based on the diffusion coefficient contrast. The method shortens the experiment time by one to four orders of magnitude. Consequently, it opens the way for high sensitivity quantification of important transient physical and chemical exchange processes such as in cellular metabolism. As a proof of principle, we demonstrate that the method reveals the structure of aggregates formed by surfactants relevant to aerosol research.

Analysis of exchange processes is time consuming by two-dimensional exchange NMR spectroscopy. Here the authors demonstrate a single-scan ultrafast Laplace NMR approach based on spatial encoding to measure molecular diffusion, with an increase by a factor six in the sensitivity per unit time.

Preparation of Long-Lived States in a Multi-Spin System by Using an Optimal Control Method

The lifetime Ts of a long-lived nuclear spin state (LLS) could be much longer than the longitudinal order T₁ . Many spin systems were used to produce long-lived states, including two or more homonuclear spins that couple to each other. For multiple homonuclear spins with rather small chemical shift difference, normally it is difficult to selectively control the spins and then to prepare a LLS. Herein, we present a scheme that prepares different spin orders in a multi-spin system by using optimal control and numerical calculation. By experimentally measuring the lifetime of the states, we find that for a three-spin physical system, although there are many forms of state combinations with different spin orders, each component has its own lifetime.

Generalised magnetisation-to-singlet-order transfer in nuclear magnetic resonance

A variety of pulse sequences have been described for converting nuclear spin magnetisation into long-lived singlet order for nuclear spin-1/2 pairs. Existing sequences operate well in two extreme parameter regimes. The magnetisation-to-singlet (M2S) pulse sequence performs a robust conversion of nuclear spin magnetisation into singlet order in the near-equivalent limit, meaning that the difference in chemical shift frequencies of the two spins is much smaller than the spin-spin coupling. Other pulse sequences operate in the strong-inequivalence regime, where the shift difference is much larger than the spin-spin coupling. However both sets of pulse sequences fail in the intermediate regime, where the chemical shift difference and the spin-spin coupling are roughly equal in magnitude. We describe a generalised version of M2S, called gM2S, which achieves robust singlet order excitation for spin systems ranging from the near-equivalence limit well into the intermediate regime. This closes an important gap left by existing pulse sequences. The efficiency of the gM2S sequence is demonstrated numerically and experimentally for near-equivalent and intermediate-regime cases.

Rotational-permutational dual-pairing and long-lived spin order

Quantum systems in contact with a thermal environment experience coherent and incoherent dynamics. These drive the system back toward thermal equilibrium after an initial perturbation. The relaxation process involves the reorganization of spin state populations and the decay of spin state coherences. In general, individual populations and coherences may exhibit different relaxation time constants. Particular spin configurations may exhibit exceptionally long relaxation time constants. Such spin configurations are known as long-lived spin order. The existence of long-lived spin order is a direct consequence of the symmetries of the system. For nuclear spin systems, rotational and permutational symmetries are of fundamental importance. Based on the Schur-Weyl duality theorem, we describe a theoretical framework for the study of rotational and permutational dual-symmetries in the context of long-lived spin order. Making use of the proposed formalism, we derive refined bounds on the number on long-lived spin populations and coherences for systems exhibiting rotational-permutational dual-symmetries.

Coherent polarization transfer in chemically exchanging systems

Simulation of the interplay of coherent polarization transfer and chemical exchange described by superoperators and Monte Carlo simulations alike.

Generating and sustaining long-lived spin states in 15N,15N'-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-¹⁵N,¹⁵N′-azobenzene. The singlet state of the ¹⁵N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the ¹⁵N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of ¹⁵N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

From LASER physics to the para-hydrogen pumped RASER

The properties of the LASER with respect to self-organization are compared with the key features of the p-H₂ pumped RASER. According to LASER theory the equations of motion for the LASER can be derived from the enslaving principle, i.e. the slowest-changing order parameter (the light field in the resonator) enslaves the rapidly relaxing atomic degrees of freedom. Likewise, it is shown here that the equations of motion for the p-H₂ pumped RASER result from a set of order parameters, where the transverse magnetization of the RASER-active spin states enslaves the electromagnetic modes. The consequences are striking for nuclear magnetic resonance (NMR) spectroscopy, since long-lasting multi-mode RASER oscillations enable unprecedented spectroscopic resolution down to the micro-Hertz regime. Based on the theory for multi-mode RASER operation we analyze the conditions that reveal either the collapse of the entire NMR spectrum, the occurrence of self-organized frequency-combs, or RASER spectra which reflect the J-coupled network of the molecule. Certain RASER experiments involving the protons of ¹⁵N pyridine or 3-picoline molecules pumped with p-H₂ via SABRE (Signal Amplification By Reversible Exchange) show either a single RASER oscillation in the time domain, giant RASER pulses or a complex RASER beat pattern. The corresponding ¹H spectra consist of one narrow line, equidistant narrow lines (frequency-comb), or highly resolved lines reporting NMR properties, respectively. Numerous applications in the areas of material sciences, fundamental physics and medicine involving high precision sensors for magnetic fields, rotational motions or molecular structures become feasible.

Long live the singlet state!

The field of long-lived states in NMR is reviewed. The relationship of long-lived-state phenomena to those associated with spin isomerism is discussed. A brief overview is given of key developments in the field of long-lived states, including chemical symmetry-switching, the role of magnetic equivalence and magnetic inequivalence, long-lived coherences, hyperpolarized NMR involving long-lived states, quantum-rotor-induced polarization, and parahydrogen-induced hyperpolarization. Current application areas of long-lived states are reviewed, and a peer into the crystal ball reveals future developments in the field.

Terminal Diazirines Enable Reverse Polarization Transfer from 15 N2 Singlets

Diazirine moieties are chemically stable and have been incorporated into biomolecules without impediment of biological activity. The ¹⁵ N₂ labeled diazirines are appealing motifs for hyperpolarization supporting relaxation protected states with long-lived lifetimes. The (-CH¹⁵ N₂ ) diazirine groups investigated here are analogues to methyl groups, which provides the opportunity to transfer polarization stored on a relaxation protected (-CH¹⁵ N₂ ) moiety to ¹ H, thus combining the advantages of long lifetimes of ¹⁵ N polarization with superior sensitivity of ¹ H detection. Despite the proximity of ¹ H to ¹⁵ N nuclei in the diazirine moiety, ¹⁵ N T₁ times of up to (4.6±0.4) min and singlet lifetimes T_s of up to (17.5±3.8) min are observed. Furthermore, we found terminal diazirines to support hyperpolarized ¹ H₂ singlet states in CH₂ groups of chiral molecules. The singlet lifetime of ¹ H singlets is up to (9.2±1.8) min, thus exceeding ¹ H T₁ relaxation time (at 8.45 T) by a factor of ≈100.

Proton Relaxometry of Long-Lived Spin Order

A study of long-lived spin order in chlorothiophene carboxylates at both high and low magnetic fields is presented. Careful sample preparation (removal of dissolved oxygen in solution, chelating of paramagnetic impurities, reduction of convection) allows one to obtain very long-lived singlet order of the two coupled protons in chlorothiophene derivatives, having lifetimes of about 130 s in D₂ O and 240 s in deuterated methanol, which are much longer than the T₁ -relaxation times (18 and 30 s, respectively, at a field B 0 =9.4 T). In protonated solvents the relaxation times become shorter, but the lifetime is still substantially longer than T 1 . In addition, long-lived coherences are shown to have lifetimes as long as 30 s. Thiophene derivatives can be used as molecular tags to study slow transport, slow dynamics and slow chemical processes, as has been shown in recent years.

Nuclear singlet multimers (NUSIMERs) with long-lived singlet states

Magnetic resonance (NMR) is a powerful tool in chemical analysis, structure determination and in medical diagnostics. Developing novel biological sensors for this field holds promise to better investigate protein structures or target diseases more efficiently. Herein, we explore nuclear spin singlet states in dendritic macromolecules as a platform molecule to develop stimuli responsive probes. We have developed a nuclear singlet multimer (NUSIMER) based on a generation 5 poly(amidoamine) dendrimer (PAMAM) which contains on average about 90 accessible nuclear spin singlet states with lifetimes up to 10-fold longer than the T 1 relaxation times (up to 10 seconds T s vs. T 1 < 0.5 seconds) in a single molecule. We demonstrate little influence on the singlet lifetime in phosphate buffer (H2O) and a high viscosity gel environment in the presence of paramagnetic oxygen. Additionally, we demonstrate an increase in singlet lifetime upon the release of a protective chemical moiety from the NUSIMER following a stimulus, whereby no change in longitudinal relaxation time is observed. The robustness and change in singlet lifetime of the NUSIMER holds promise for the development of a novel type of biosensors.

Assessment of heteronuclear long-lived states at ultralow magnetic fields

A study of long-lived spin states in hetero-nuclear spin systems is presented.

Singlet excitation in the intermediate magnetic equivalence regime and field-dependent study of singlet–triplet leakage

Measuring field-dependence of singlet lifetimes in the intermediate magnetic equivalence regime.

Applications of dissolution dynamic nuclear polarization in chemistry and biochemistry

Sensitivity of detection is one of the most limiting aspects when applying NMR spectroscopy to current problems in the molecular sciences. A number of hyperpolarization methods exist for increasing the population difference between nuclear spin Zeeman states and enhance the signal-to-noise ratio by orders of magnitude. Among these methods, dissolution dynamic nuclear polarization (D-DNP) is unique in its capability of providing high spin polarization for many types of molecules in the liquid state. Originally proposed for biomedical applications including in vivo imaging, applications in high resolution NMR spectroscopy are now emerging. These applications are the focus of the present review. Using D-DNP, a small sample aliquot is first hyperpolarized as a frozen solid at low temperature, followed by dissolution into the liquid state. D-DNP extends the capabilities of liquid state NMR spectroscopy towards shorter timescales and enables the study of nonequilibrium processes, such as the kinetics and mechanisms of reactions. It allows the determination of intermolecular interactions, in particular based on spin relaxation parameters. At the same time, a challenge in the application of this hyperpolarization method is that spin polarization is nonrenewable. Substantial effort has been devoted to develop methods for enabling rapid correlation spectroscopy, the measurement of time-dependent signals, and the extension of the observable time window. With these methods, D-DNP has the potential to open new application areas in the chemical and biochemical sciences.

Using optimal control methods with constraints to generate singlet states in NMR

A method is proposed for optimizing the performance of the APSOC (Adiabatic-Passage Spin Order Conversion) technique, which can be exploited in NMR experiments with singlet spin states. In this technique magnetization-to-singlet conversion (and singlet-to-magnetization conversion) is performed by using adiabatically ramped RF-fields. Optimization utilizes the GRAPE (Gradient Ascent Pulse Engineering) approach, in which for a fixed search area we assume monotonicity to the envelope of the RF-field. Such an approach allows one to achieve much better performance for APSOC; consequently, the efficiency of magnetization-to-singlet conversion is greatly improved as compared to simple model RF-ramps, e.g., linear ramps. We also demonstrate that the optimization method is reasonably robust to possible inaccuracies in determining NMR parameters of the spin system under study and also in setting the RF-field parameters. The present approach can be exploited in other NMR and EPR applications using adiabatic switching of spin Hamiltonians.

Nuclear spin singlet states as magnetic on/off probes in self-assembling systems

Nuclear singlet states in thermo-responsive peptides are introduced as magnetic on/off switches.

Singlet-assisted diffusion-NMR (SAD-NMR): redefining the limits when measuring tortuosity in porous media

Long-lived singlet order is exploited in diffusion NMR experiments to successfully measure the tortuosity of randomly packed spheres with diameters ranging from 500 to 1000 μm.

Dipolar relaxation mechanism of long-lived states of methyl groups

We analyze the symmetry properties of the dipolar Hamiltonian as the main relaxation mechanism responsible for the observed NMR spectra of long-lived states of methyl groups. Long-lived states exhibit relaxation times that are considerably longer than the spin-lattice relaxation time, T 1 . The analysis is complementary to previous studies and provides insight into the relaxation mechanism of long-lived states by focusing exclusively on the symmetry of the spin Hamiltonian. Our study shows that the dipole-dipole coupling between protons of a methyl group and between the protons and an external spin are both symmetry breaking interactions that can lead to relaxation pathways that transform the polarization from symmetry order to Zeeman order. The net contribution of the internal dipolar interaction to the NMR observation of long-lived states is zero. Our calculation is in good agreement with the reported features of the observed spectra and previous theoretical studies.

Accessing the long-time limit in diffusion NMR: The case of singlet assisted diffusive diffraction q-space

The latest developments in the field of long-lived spin states are merged with pulsed-field gradient techniques to extend the diffusion time beyond what is currently achievable in standard q-space diffusive-diffraction studies. The method uses nearly-equivalent spin-1/2 pairs that let diffusion times of the order of many minutes to be measured allowing access to the long-time limit in cavities of macroscopic size (millimeters). A pulse sequence suitable to exploit this regime has been developed and validated with the use of numerical simulations and experiments.

Bang-bang optimal control of large spin systems: Enhancement of 13C-13C singlet-order at natural abundance

Using a bang-bang optimal control technique, we transfer polarization from a set of abundant high-γ nuclei directly to singlet order of a low-γ spin-pair. This approach is analogous to algorithmic cooling (AC) procedure used in quantum state purification. Specifically, we apply this method for enhancing the singlet order in a natural abundant ¹³C- ¹³C spin pair by exploiting nine equivalent protons of an 11-spin system. Compared to the standard method not involving polarization transfer, we find an enhancement of singlet order by about 3.4 times. In addition, since the singlet magnetization is contributed by the faster relaxing protons, the recycle delay is halved. Thus effectively we observe a reduction in the overall experimental time by a factor of 23. We also discuss a possible extension of AC, known as heat-bath algorithmic cooling (HBAC).

Effect of convection and B1 inhomogeneity on singlet relaxation experiments

Nuclear spin singlet lifetimes can often exceed the T₁ length scales by a large factor. This property makes them suitable for polarization storage. The measurement of such long lifetimes itself can become challenging due to the influence of even very weak relaxation mechanisms. Here we show that a judicious choice of the singlet-to-triplet conversion method is highly important in order to achieve reliable singlet relaxation measurements. In particular, we identify thermal convection, in connection with B₁ field gradients, asa significant apparent decay mechanism, which limits the ability to measure the true singlet state lifetimes. Highly B₁-compensated broadband singlet excitation/detection sequences are shown to minimize the influence of macroscopic molecular motion and B₁ inhomogeneity.

Singlet NMR methodology in two-spin-1/2 systems

This paper discusses methodology developed over the past 12years in order to access and manipulate singlet order in systems comprising two coupled spin-1/2 nuclei in liquid-state nuclear magnetic resonance. Pulse sequences that are valid for different regimes are discussed, and fully analytical proofs are given using different spin dynamics techniques that include product operator methods, the single transition operator formalism, and average Hamiltonian theory. Methods used to filter singlet order from byproducts of pulse sequences are also listed and discussed analytically. The theoretical maximum amplitudes of the transformations achieved by these techniques are reported, together with the results of numerical simulations performed using custom-built simulation code.

Versatile magnetic resonance singlet tags compatible with biological conditions

The long lifetime of nuclear singlet states holds promise for the development of molecular tracers to study motional processes in proteins with increased precision or to act as imaging contrast agents.

Improving accuracy in DOSY and diffusion measurements using triaxial field gradients

NMR measurements of diffusion in solution, whether primarily quantitative, or, (as in DOSY, Diffusion-Ordered Spectroscopy) qualitative, can be particularly demanding. Here we show how the use of appropriate transverse (x, y) pulsed field gradients, orthogonal to the more usual z axis pulsed field gradient applied along the long axis of the sample, can greatly reduce two important sources of systematic error in diffusion experiments. These are the extra signal attenuation caused by sample convection, and gradient-dependent signal phase shifts caused by the magnetic field and field-frequency lock disturbances generated by field gradient pulses.

Probing scalar coupling differences via long-lived singlet states

We probe small scalar coupling differences via the coherent interactions between two nuclear spin singlet states in organic molecules. We show that the spin-lock induced crossing (SLIC) technique enables the coherent transfer of singlet order between one spin pair and another. The transfer is mediated by the difference in syn and anti vicinal or long-range J couplings among the spins. By measuring the transfer rate, we calculate a J coupling difference of 8±2mHz in phenylalanine-glycine-glycine and 2.57±0.04Hz in glutamate. We also characterize a coherence between two singlet states in glutamate, which may enable the creation of a long-lived quantum memory.

Synthesis of an isotopically labeled naphthalene derivative that supports a long-lived nuclear singlet state

The synthesis of an octa-alkoxy substituted isotopically labeled naphthalene derivative, shown to have excellent properties in singlet NMR experiments, is described. This highly substituted naphthalene system, which incorporates an adjacent ¹³C spin pair, is readily accessed from a commercially available ¹³C₂-labeled building block via sequential thermal alkynyl- and arylcyclobutenone rearrangements. The synthetic route incorporates a simple desymmetrization approach leading to a small difference in the chemical shifts of the ¹³C spin pair, a design constraint crucial for accessing nuclear singlet order.

Real-space imaging of macroscopic diffusion and slow flow by singlet tagging MRI

Magnetic resonance imaging can be used to study motional processes such as flow and diffusion, but the accessible timescales are limited by longitudinal relaxation. The spatially selective conversion from magnetization to long-lived singlet order in designer molecules makes it possible to tag a region of interest for an extended period of time, of the order of several minutes. Here we exploit this concept of "singlet tagging" to monitor diffusion over a macroscopic scale as well as very slow flow.

Systematic bias in NMR diffusion measurements on polydisperse systems

Least-squares fitting of the Stejskal-Tanner equation is a routine process in the measurement of molecular diffusion coefficient (MDC) using Nuclear Magnetic Resonance (NMR) Spectroscopy. It is simple and elegant. However, a bias of the MDC is noticed when the system is polydispersed. This is due to improper accounts of the diffusion coefficient distribution. Eventually, it leads to a discrepancy between the observed MDC and the statistical mean value of the distribution. To reveal the discrepancy, an analytical solution is derived when the diffusion data is taken a logarithmic linearization. Computer simulation is also applied to obtain a non-linear regression result. For a Gaussian distribution of the MDCs, the bias is proportional to the square of the distribution width (linear regression), but it is also inversely proportional to the statistical mean value of the distribution (non-linear regression). This indicates that the MDC derived from Stejskal-Tanner equation only holds well for narrow distribution of MDCs. Otherwise, molecular radius derived from the Stokes-Einstein equation needs to be reconsidered due to the incorrect estimation of the MDC.